Using Wave Modifier instances in Animation node
Actions in Animation Nodes are abstractions of F-Curves, or possibly other data. So actions are not effective when it comes to animations that depends solely on data such as the current frame in this case.

If I understand what you want to do correctly, you can use the time offset parameter of the wave modifier. So, instance your objects using the Copy Full Object option to copy the modifiers from the source object to the instance, and modulate the time offset parameter using an attribute output node as follows:



Ghosting Value

What you can do is set the pass index of object to an arithmetic sequence, then in the shader, sample the object's pass index, and divide it by the number of instances as follows: